Nature of problem:Hadronic two-photon reactions in a new energy domain are becoming
accessible with LEP2. Unlike purely electroweak processes, hadronic
processes contain dominant non-perturbative components parametrized by
suitable structure functions, which are functions of the two-photon
invariant mass W and the photon virtualities Q1 and Q2. It is hence
advantageous to have a Monte Carlo program that can generate events with
the possibility to keep W and, optionally, Qi at fixed, user-defined
values. Moreover, at least one program with an exact treatment of both
the kinematics and the dynamics over the whole range
m**2 >> m**2(W/sqrt(s))**4 ~< s (m is the electron mass and sqrt(s) the
e+e- c.m. energy) is needed, (i) to check the various approximations
used in other programs, and (ii) to be able to explore additional
information on the hadronic physics, e.g. coded in azimuthal
dependences.

Solution method:The differential cross section for e+e- -> e+e-X at given two-photon
invariant mass W is rewritten in terms of four invariants with the
photon virtualities Qi as the two outermost integration variables (next
to W), in order to simultaneously cope with antitagged and tagged
electron modes. Due care is taken of numerically stable expressions
while keeping all electron-mass and Qi dependences. Special attention
is devoted to the azimuthal dependences of the cross section. Cuts on
the scattered electrons are to a large extent incorporated analytically
and suitable mappings introduced to deal with the peaking structure of
the differential cross section. The event generation yields either
weighted events or unweighted ones (i.e. equally weighted events with
weight 1), the latter based on the hit-or-miss technique. Optionally,
VEGAS [1] can be invoked to (i) obtain an accurate estimate of the
integrated cross section and (ii) improve the event generation
efficiency through additional variable mappings provided by the grid
information of VEGAS. The program is set up so that additional hadronic
(or leptonic) reactions can easily be added.
Other subprograms used: VEGAS, RANLUX [2], HBOOK [3] and DATIME [4].

Summary of revisions:Differences with earlier version [5]

The W-integrated total e+e- cross section sigma can now be
calculated besides dsigma/dW**2 and d2sigma/dW**2dQ22.

The program can be used to calculate sigma for a total, Regge-like
hadronic cross section as well as the effective two-photon luminosity
function L defined by
sigma = integral(dtau L(tau) sigmagammagamma (tau s)), where
sigmagammagamma is the real-photon cross section. In both cases four
different ansatze for the Qi dependence of the hadronic form factors is
provided.

The total two-photon cross section at large Qi**2 calculated in
perturbative QCD, in terms of the BFKL Pomeron, is incorporated.

Structure functions for the formation of resonances in two-photon
collisions are included for 30 mesons, light or heavy. One can choose
between two models: in one, the full, non-trivial Q1**2, Q2**2
correlations as given in the constituent quark model are kept. The
alternative model is based on a factorized VMD-inspired ansatz.

Running time:The integration time depends on the required cross section accuracy and
the applied cuts. For instance, 13 seconds on an IBM RS/6000 yields an
accuracy of the VEGAS integration of about 0.1 per cent for the antitag
mode or of about 0.2 per cent for a typical single-tag mode; within the
same time the error of the simple Monte Carlo integration is about 0.5
per cent for either mode. Event generation with or without VEGAS
improvement and for either tag mode takes about 4x10**-4 (2x10**-3)
seconds per event for weighted (unweighted) events.